[RUME] Mathematical proofs becoming harder to verify?

[Cathy Kessel]

Chronologically between Kitcher and Fauvel & Gray, is De Millo,  
Richard A., Lipton, Richard J., & Perlis, Alan J. (1986). Social  
processes and
proofs of theorems and programs. In Thomas Tymoczko (Ed.), New  
directions in the
philosophy of mathematics (pp. 267-285). Boston: Birkhauser. (The  
Tymoczko book is generally interesting and has a discussion of the  
philosophical significance of the 4-color theorem.)

There was also the "death of proof" controversy: Horgan, J. (1993).  
The Death of Proof.
Scientific American, 269(4), 93-103

--Cathy


On Feb 20, 2006, at 7:48 PM, Jered Wasburn-Moses wrote:

> Jennifer:
>
> I don't think that this is a new claim. Gila Hanna is perhaps the most
> consistent, but by no means the only, writer making a similar claim  
> for some
> time. (The first sentence you quote is quite problematic,  
> incidentally, as
> Hanna and others would argue!)
>
> Frequently cited mathematical events include the proof (?) of the 4- 
> color
> theorem and the classification of finite groups.
>
> You also might look at something like Kitcher's The Nature of  
> Mathematical
> Knowledge (1983), which is somewhat outdated in this regard but still
> informative, or the slightly more recent History of Mathematics: A  
> Reader
> (1987) by Fauvel and Gray.
>
> Hope this helps,
> --Jered
>
>
> --- Jennifer Smith <jenn.smith at mail.utexas.edu> wrote:
>
>
>> A colleague sent this URL to me, and I am really curious to hear  
>> what others
>> think!
>>
>> Title: Mathematical Proofs Getting Harder to Verify
>>
>> Excerpt:
>>
>> A mathematical proof is irrefutably true, a manifestation of pure  
>> logic. But
>> an increasing number of mathematical proofs are now impossible to  
>> verify
>> with absolute certainty, according to experts in the field.
>>
>> "I think that we're now inescapably in an age where the large  
>> statements of
>> mathematics are so complex that we may never know for sure whether  
>> they're
>> true or false," says Keith Devlin of Stanford University in  
>> California, US.
>> "That puts us in the same boat as all the other scientists."
>>
>> Link to story: http://www.newscientist.com/channel/fundamentals/ 
>> dn8743.html
>>
>> --
>> Jennifer Christian Smith
>> Assistant Professor
>> Center for Science and Mathematics Education
>> The University of Texas at Austin
>> Office: (512) 232-9682
>> Fax: (512) 471-8460
>> Home page: http://teachnet.edb.utexas.edu/~jenn_smith
>> <http://teachnet.edb.utexas.edu/%7Ejenn_smith>
>> AIM: drjennsmith
>>
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